1. Field of the Invention
The present invention relates to a voltage-controlled oscillator, and more particularly, to a capacitive-degeneration double cross-coupled voltage-controlled oscillator capable of increasing a MAOF (maximum attainable oscillation frequency) and decreasing an input capacitance.
2. Description of the Related Art
Recently, as demands for millimeter-wave band frequency resources increase, associated wire/wireless communication devices have been actively developed.
Particularly, due to an increase in processing speeds of silicon devices, conventional expensive millimeter-wave compound semiconductor monolithic microwave integrated circuit (MMIC) devices are gradually replaced with inexpensive silicon millimeter-wave MMIC devices.
However, only the development of the silicon millimeter-wave MMIC is reported, but performance of the silicon is lower than that of the compound semiconductor MMIC in terms of noise and gain characteristics.
In addition, unlike the compound semiconductor, since the silicon substrate has large loss, the silicon substrate causes serious problems such signal leakage and interference in millimeter-wave band.
Therefore, various circuit design technique for solving the problems of the silicon semiconductor in millimeter-wave band have been researched.
A low noise/low power consumption voltage-controlled oscillator is one of the important components of millimeter-wave band wire/wireless communication system. A voltage-controlled oscillator widely used for a silicon integrated circuit includes an LC resonator and negative resistance cells that are constructed as a simple cross-coupled pair. A negative resistance generated by the cross-coupled pair compensates for a loss of the LC resonator, so that oscillation can be generated and sustained.
However, since the simple cross-coupled pair has a small MAOF and a large input capacitance, the simple cross-coupled pair cannot be easily applied to the millimeter-wave voltage-controlled oscillator.
The MAOF is defined as a frequency at which a negative resistance becomes zero when the negative resistance is increased from a negative region to a positive region. That is, the MAOF is a maximum frequency among frequencies at which the negative resistance occurs. As a result, the voltage-controlled oscillator having an oscillation frequency higher than the MAOF cannot be designed.
In addition, as the input capacitance of the cross-coupled pair is increased, a capacitance, coupling with LC resonator and determining a resonance frequency, is also increased. Therefore, the oscillation frequency is lowered.
Furthermore, since modeling accuracy of active and passive devices including inductor, varactor, and transistor becomes lowered in millimeter-wave band, a voltage-controlled oscillator designed and manufactured by using the simple cross-coupled pair may neither obtain a desired oscillation frequency nor oscillate.
In order to increase the MAOF and decrease the input capacitance of the simple cross-coupled pair, a capacitive-degeneration cross-coupled pair has been developed.
In the capacitive-degeneration cross-coupled pair structure, emitters of cross-coupled pair transistors are connected to each other through a capacitance, or the emitters of the cross-coupled pair transistors are connected to ground through a capacitance. As a result, it is possible to increase the MAOF and decrease the input capacitance of the cross-coupled pair.
Although the capacitive-degeneration cross-coupled pair voltage-controlled oscillator uses the cross-coupled pair structure, the MAOF or input capacitance cannot be satisfactorily improved in comparison with the simple cross-coupled pair.
FIGS. 1A and 1B are circuit diagrams illustrating a conventional simple cross-coupled voltage-controlled oscillator 100.
Referring to FIG. 1A, the conventional voltage-controlled oscillator 100 includes a resonating unit 110 and an oscillating unit 120.
The resonating unit 110 includes a supply voltage Vcc, first and second inductors Lr1 and Lr2 commonly connected to the supply voltage Vcc, and a varactor capacitance Cr and a parasitic resistance Rr which are connected in parallel to the first and second inductors Lr1 and Lr2.
The oscillating unit 120 includes first and second transistors Q1 and Q2 which are connected to respective ends of the parasitic resistance Rr and of which collectors and bases are cross-coupled to each other and a current source Is connected to emitters of the first and second transistors Q1 and Q2.
FIG. 1B is a circuit diagram illustrating a small-signal equivalent circuit of the simple cross-coupled oscillating unit 120 of FIG. 1A.
In FIG. 1B,
      β    ⁡          (      ω      )        =      -          j      ⁡              (                              ω            T                    ω                )            denotes a high-frequency small-signal current gain, and gm, re, rb, and ib denote a transconductance, an emitter resistance, an intrinsic base resistance, and a base current of a transistor, respectively.
Input admittances Yin, that is, an input resistance Rin and an input capacitance Cin of the circuit of FIG. 1B can be represented by Equations 1 and 2, respectively.
                              R                      i            ⁢                                                  ⁢            n                          =                                            2              ⁢                                                (                                                            r                      b                                        +                                          r                      e                                                        )                                2                                      +                          2              ⁢                                                (                                                            ω                      T                                        ω                                    )                                2                            ⁢                                                (                                                            1                                              g                        m                                                              +                                          r                      e                                                        )                                2                                                                        (                                                r                  b                                +                                  r                  e                                            )                        -                                                            (                                                            ω                      T                                        ω                                    )                                2                            ⁢                              (                                                      1                                          g                      m                                                        +                                      r                    e                                                  )                                                                        [                  Equation          ⁢                                          ⁢          1                ]            
                              C                      i            ⁢                                                  ⁢            n                          =                                            (                                                ω                  T                                                  ω                  2                                            )                        ⁢                          (                                                1                                      g                    m                                                  +                                  r                  b                                +                                  2                  ⁢                                      r                    e                                                              )                                                          2              ⁢                                                (                                                            r                      b                                        +                                          r                      e                                                        )                                2                                      +                          2              ⁢                                                (                                                            ω                      T                                        ω                                    )                                2                            ⁢                                                (                                                            1                                              g                        m                                                              +                                          r                      e                                                        )                                2                                                                        [                  Equation          ⁢                                          ⁢          2                ]            
Here,
            ω      T        =                  2        ⁢        π        ⁢                                  ⁢                  f          T                    =                        g          m                                      C            π                    +                      C            μ                                ,and fT, gm, rb, and re denote a maximum transition frequency, a transconductance, an intrinsic base resistance, and an emitter resistance of a transistor, respectively.
Since the MAOF ftrans is a frequency at which a negative resistance becomes zero when an input negative resistance is increased from a negative region to a positive region, the MAOF ftrans represented by Equation 3 can be calculated from Equation 1.
                              f          T                ⁢                                                            r                e                            +                              1                                  g                  m                                                                                    r                b                            +                              r                e                                                                        [                  Equation          ⁢                                          ⁢          3                ]            
Since the simple cross-coupled oscillating unit 120 has a simple structure and easily generates a differential signal, the simple cross-coupled oscillating unit 120 is widely used for an integrated circuit. However, as seen in Equation 3, the simple cross-coupled oscillating unit 120 has a problem in that the MAOF ftrans is limited due to the intrinsic base resistance rb of the transistor.
In addition, due to a base-emitter capacitance, a base-collector capacitance, and a base-substrate capacitance of each transistor, the voltage-controlled oscillator of FIG. 1 has such problems as a large input capacitance and a lower oscillation frequency.
In order to solve the above-mentioned problems, a new-type capacitive-degeneration cross-coupled voltage-controlled oscillator capable of increasing the MAOF ftrans and decreasing the input capacitance by using a degeneration capacitance has been proposed.
FIG. 2A is a circuit diagram illustrating a conventional capacitive-degeneration cross-coupled voltage-controlled oscillator.
Referring to FIG. 2A, the capacitive-degeneration cross-coupled voltage-controlled oscillator 200 includes a resonating unit 210 and an oscillating unit 220.
The resonating unit 210 includes a supply voltage Vcc, first and second inductors Lr1 and Lr2 commonly connected to the supply voltage Vcc, and a varactor capacitance Cr and respective ends of the parasitic resistance Rr and of which are connected in parallel to the first and second inductors Lr1 and Lr2.
The oscillating unit 220 includes first and second transistors Q1 and Q2 which are connected to respective ends of the parasitic resistance Rr and of which collectors and bases are cross-coupled to each other, a degeneration capacitance Cd connected between emitters of the first and second transistors Q1 and Q2, and a current source Is connected to emitters of the first and second transistors Q1 and Q2.
Unlike the simple cross-coupled voltage-controlled oscillator 100 of FIG. 1A, in the capacitive-degeneration cross-coupled voltage-controlled oscillator 200 of FIG. 2A, the degeneration capacitance Cd is connected between the emitters of the first and second transistors Q1 and Q2, so that a negative resistance of the oscillating unit 220 can be increased.
Accordingly, in the capacitive-degeneration cross-coupled voltage-controlled oscillator, since the negative resistance of the oscillating unit 220 can be increased, the increased negative resistance compensates for a loss of the resonating unit 210, so that oscillation can be generated and sustained.
In addition, due to the newly added component, that is, the degeneration capacitance Cd, in the oscillating unit 220, the first transistor Q1, the degeneration capacitance Cd, and the second transistor Q2 constitutes a positive feedback loop.
Therefore, the input capacitance Cin of the oscillating unit 220 can be intuitively represented by Equation 4.
                              1                                    1                                                C                                      be                    2                                                  ⁢                                                                                        +                          1                              2                ⁢                                  C                  d                                                                    ⁢                                  ⁢        or        ⁢                                  ⁢                  1                                    1                                                C                                      be                    1                                                  ⁢                                                                                        +                          1                              2                ⁢                                  C                  d                                                                                        [                  Equation          ⁢                                          ⁢          4                ]            
Here, Cbe1 denotes a base-emitter capacitance of the first transistor Q1, and Cbe2 denotes a base-emitter capacitance of the second transistor Q2.
That is, the input capacitance Cin of the oscillating unit 220 of FIG. 2 is inverse proportion to 1/(2Cd) due to the degeneration capacitance Cd.
More specifically, input admittances Yin, that is, an input resistance Rin and an input capacitance Cin can be exactly represented by Equations 5 and 6, respectively.
                              R                      i            ⁢                                                  ⁢            n                          =                                                                                                                        2                      ⁡                                              [                                                                              (                                                                                          r                                b                                                            +                                                              r                                e                                                                                      )                                                    -                                                                                    (                                                                                                ω                                  T                                                                ω                                                            )                                                        ⁢                                                          1                                                              2                                ⁢                                ω                                ⁢                                                                                                                                  ⁢                                                                  C                                  d                                                                                                                                                                    ]                                                              2                                    +                                                                                                                          2                    ⁡                                          [                                                                                                    (                                                                                          ω                                T                                                            ω                                                        )                                                    ⁢                                                      (                                                                                          1                                                                  g                                  m                                                                                            +                              r                                                        )                                                                          +                                                  1                                                      2                            ⁢                            ω                            ⁢                                                                                                                  ⁢                                                          C                              d                                                                                                                          ]                                                        2                                                                                        (                                                r                  b                                +                                  r                  e                                            )                        -                                                            (                                                            ω                      T                                        ω                                    )                                2                            ⁢                              (                                                      1                                          g                      m                                                        +                                      r                    e                                    +                                      1                                                                  ω                        T                                            ⁢                                              C                        d                                                                                            )                                                                        [                  Equation          ⁢                                          ⁢          5                ]            
                              C                      i            ⁢                                                  ⁢            n                          =                                            (                                                ω                  T                                                  ω                  2                                            )                        ⁡                          [                                                (                                                            r                      b                                        +                                          2                      ⁢                                              r                        e                                                              +                                          1                                              g                        m                                                                              )                                +                                  1                                      2                    ⁢                                          ω                      T                                        ⁢                                          C                      d                                                                      -                                                      (                                                                  ω                        T                                            ω                                        )                                    ⁢                                      1                                          2                      ⁢                      ω                      ⁢                                                                                          ⁢                                              C                        d                                                                                                        ]                                                                                                                                      2                      ⁡                                              [                                                                              (                                                                                          r                                b                                                            +                                                              r                                e                                                                                      )                                                    -                                                                                    (                                                                                                ω                                  T                                                                ω                                                            )                                                        ⁢                                                          1                                                              2                                ⁢                                ω                                ⁢                                                                                                                                  ⁢                                                                  C                                  d                                                                                                                                                                    ]                                                              2                                    +                                                                                                                          2                    ⁡                                          [                                                                        1                                                      2                            ⁢                            ω                            ⁢                                                                                                                  ⁢                                                          C                              d                                                                                                      +                                                                              (                                                                                          ω                                T                                                            ω                                                        )                                                    ⁢                                                      (                                                                                          1                                                                  g                                  m                                                                                            +                                                              r                                e                                                                                      )                                                                                              ]                                                        2                                                                                        [                  Equation          ⁢                                          ⁢          6                ]            
The MAOF ftrans of the capacitive-degeneration cross-coupled oscillating unit 220 represented by Equation 7 can be calculated from Equation 5. As seen in Equation 7, the MAOF ftrans is in proportion to a square root of 1/(Cd).
                              f          trans                =                              f            T                    ⁢                                                                      r                  e                                +                                  1                                      g                    m                                                  +                                  1                                                            ω                      T                                        ⁢                                          C                      d                                                                                                  (                                                      r                    b                                    +                                      r                    e                                                  )                                                                        [                  Equation          ⁢                                          ⁢          7                ]            
Here,
            ω      T        =                  2        ⁢        π        ⁢                                  ⁢                  f          T                    =                        g          m                                      C            π                    +                      C            μ                                ,and fT, gm, rb, and re denote a maximum transition frequency, a transconductance, an intrinsic base resistance, and an emitter resistance of a transistor.
However, the capacitive-degeneration voltage-controlled oscillator 200 has a problem in that the negative resistance disappears when the degeneration capacitance Cd is too small or 0.
In addition, since the capacitive-degeneration voltage-controlled oscillator 200 can adjust the MAOF ftrans or the input capacitance Cin by using only the degeneration capacitance Cd, a satisfactory performance cannot be obtained in comparison with a simple cross-coupled pair voltage-controlled oscillator.